Finite Group Databasebeta

← #11791442

Subgroups — #11791442

Order 1152.

538 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593909C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3C2×#63730C214yesmaximal
4#10590331C211yesmaximal, characteristic
5C2×#3797C2212yes—
6C2×C4⋊#157C2212yes—
7C2×C4×#157—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#869—21no—
10#63919C412yescomplemented
11#63919C412yescomplemented
12#63900—21no—
13#63900—21no—
14#63873—21no—
15C2×#3710C2212yes—
16#63781—21no—
17#63730—28no—
18C3×C4⋊(C3⋊C8)—21no—
19#63572—21no—
20D3×C4⋊Q8—61no—
21D3×C4⋊C8—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×C3×Dic6—22no—
27C2×#627C2×C414yes—
28C2×#624—22no—
29#3797—24no—
30#3797—24no—
31C4⋊#157—22no—
32C4⋊#157D414yes—
33C4×#157—42no—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C3×C4⋊Dic3—22no—
39C3×C4⋊Dic3—22no—
40C2×C3×C3⋊C8—22no—
41#3724—22no—
42#3724—22no—
43#3710—24no—
44#1981—91nomaximal, Sylow
45C2×D3×Q8—62no—
46C3×C4⋊Q8—61no—
47#944—62no—
48C2×D3×C8—62no—
49D3×C4⋊C4—62no—
50D3×C4⋊C4—62no—
51#888—62no—
52#888—62no—
53C42×D3—61no—
54C42×D3—61no—
55#869—21no—
56C3×C4⋊C8—61no—
57Dic3⋊C8—62no—
58C4⋊(C3⋊C8)—21no—
59C22×C3⋊D3C2×D411yescharacteristic
60C2×#157—24no—
61C2×#157—42no—
62C2×#157—42no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C4×C3⋊D3—22no—
70C4×C3⋊D3SD1612yes—
71C4×C3⋊D3Q1612yes—
72C4×C3⋊D3C2×D412yes—
73C4×C3⋊D3#4112yes—
74C2×C3×Dic3—24no—
75C3×Dic6—42no—
76C3×Dic6—42no—
77#627—28no—
78#624—44no—
79C3×C3⋊C8—42no—
80C2×C4⋊Q8—91no—
81C2×C4⋊C8—91no—
82C2×#103—94no—
83C4×C4⋊C4—91no—
84C2×C3×Q8—62no—
85D3×Q8—124no—
86D3×Q8—124no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—61no—
93C2×C4×D3—64no—
94C2×Dic6—22no—
95C2×Dic6—64no—
96C2×C3×C8—62no—
97C3×C4⋊C4—62no—
98C3×C4⋊C4—62no—
99C3×C42—21no—
100C3×C42—21no—
101C4⋊Dic3—22no—
102C4⋊Dic3—22no—
103Dic3⋊C4—64no—
104Dic3⋊C4—64no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C2×C3⋊C8—22no—
112D3×C8—124no—
113C22×C32C2×C22⋊C411yescharacteristic
114C2×C3⋊D3#12112yes—
115C2×C3⋊D3C2×SD1611yescharacteristic
116C2×C3⋊D3C2×Q1611yescharacteristic
117C2×C3⋊D3#13712yes—
118#157—44no—
119C32×C4—21no—
120C32×C4#10312yescomplemented
121C32×C4#12411yescharacteristic
122C32×C4#12711yescharacteristic
123C3⋊Dic3—21no—
124C3⋊Dic3#10312yescomplemented
125C3⋊Dic3C4×D412yes—
126C3×Dic3—44no—
127C22×Q8—92no—
128C22×C8—92no—
129C4⋊Q8—61no—
130C4⋊Q8—92no—
131C4⋊Q8—92no—
132C4⋊Q8—181no—
133C2×C4⋊C4—92no—
134C2×C4⋊C4—181no—
135C2×C4⋊C4—181no—
136C2×C42—91no—
137C2×C42—181no—
138C4⋊C8—61no—
139C4⋊C8—181no—
140#103—188no—
141#95—181no—
142C22×D3—61no—
143C22×D3—61no—
144C3×Q8—122no—
145C3×Q8—122no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—64no—
153C2×Dic3—24no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—64no—
169C4×D3—122no—
170C4×D3—128no—
171Dic6—42no—
172Dic6—42no—
173Dic6—128no—
174C3×C8—122no—
175C3⋊C8—42no—
176C2×C32#39011yescharacteristic
177C2×C32C2×#10311yescharacteristic
178C2×C32#41911yescharacteristic
179C3⋊D3#46112yes—
180C3⋊D3#46212yes—
181C2×Q8—62no—
182C2×Q8—94no—
183C2×Q8—184no—
184C2×Q8—184no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—182no—
189C22×C4—182no—
190C2×C8—62no—
191C2×C8—184no—
192C4⋊C4—62no—
193C4⋊C4—62no—
194C4⋊C4—94no—
195C4⋊C4—182no—
196C4⋊C4—182no—
197C4⋊C4—182no—
198C42—91no—
199C42—91no—
200C42—91no—
201C42—362no—
202C42GO+(4,𝔽2)11yescharacteristic
203C22×C3—21no—
204C22×C3—21no—
205C2×D3—62no—
206C2×D3—62no—
207C2×D3—61no—
208C2×D3—61no—
209C2×D3—61no—
210C2×D3—61no—
211C2×D3—62no—
212C2×D3—62no—
213C3×C4—22no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—41no—
221C3×C4—124no—
222Dic3—44no—
223Dic3—62no—
224Dic3—62no—
225Dic3—62no—
226Dic3—62no—
227Dic3—62no—
228Dic3—121no—
229C32#198111yescharacteristic, complemented, Sylow
230C23—91no—
231Q8—122no—
232Q8—122no—
233Q8—188no—
234C2×C4—64no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—92no—
238C2×C4—92no—
239C2×C4—92no—
240C2×C4—92no—
241C2×C4—91no—
242C2×C4—182no—
243C2×C4—184no—
244C2×C4—364no—
245C2×C4—362no—
246C2×C4—362no—
247C2×C4D32⋊C411yescharacteristic
248C2×C4D32⋊C411yescharacteristic
249C2×C4C2×GO+(4,𝔽2)11yescharacteristic
250C8—122no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257D3—62no—
258D3—62no—
259D3—62no—
260D3—62no—
261C22—91no—
262C22—91no—
263C22—92no—
264C22—92no—
265C22C2×D32⋊C411yescharacteristic
266C4—21no—
267C4—92no—
268C4—92no—
269C4—124no—
270C4—181no—
271C4—364no—
272C4#6373012yescomplemented
273C4#6422111yescharacteristic
274C4#6423111yescharacteristic
275C3—21no—
276C3—21no—
277C2—92no—
278C2—92no—
279C2C2×#6373011yescharacteristic
280C2#1059332111yescharacteristic
281C2#1059340711yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1981
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
10. #63919C4semidirect
11. #63919C4semidirect
120. C32×C4#103semidirect
124. C3⋊Dic3#103semidirect
229. C32#1981semidirect
272. C4#63730semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105939092
C4×C4⋊#1572
C2×#637302
#105903312
#19819